Did you miss the part where Finn needed someone to fly the Tie Fighter? (Not having flight training is a good way to prevent defections.) And I doubt the New Order bothers treating troops who go mental in the hopes they return to duty. They probably just shoot them.
If he did so well in training that he was placed immediately into an elite unit (with no prior experience), would they really be so quick to kill such a valuable commodity? 😉
You’re the one who brought up that Finn should fake having mental problems. 😉